ProjectiveVariety -- the class of all projective varieties

Functions and methods returning a projective variety:

• ambient(ProjectiveVariety) -- see ambient(AffineVariety) -- the ambient affine or projective space of an embedded variety
• Proj -- make a projective variety
• singularLocus(ProjectiveVariety) -- see singularLocus(AffineVariety) -- the locus of singular points in a variety

Methods that use a projective variety:

• canonicalBundle(ProjectiveVariety) -- see canonicalBundle -- the canonical bundle of a projective variety
• char(ProjectiveVariety) -- see char(AffineVariety) -- the characteristic of the coordinate ring of a variety
• cotangentSheaf(ProjectiveVariety) -- see cotangentSheaf -- cotangent sheaf of a projective variety
• cotangentSheaf(ZZ,ProjectiveVariety) -- exterior powers of the cotangent sheaf of a projective variety
• degree(ProjectiveVariety)
• dim(ProjectiveVariety) -- dimension of the projective variety
• euler(ProjectiveVariety) -- topological Euler characteristic of a (smooth) projective variety
• genera(ProjectiveVariety)
• genus(ProjectiveVariety)
• hh(Sequence,ProjectiveVariety) -- see hh -- Hodge numbers of a smooth projective variety
• HH^ZZ(ProjectiveVariety,SumOfTwists) -- see HH^ZZ SumOfTwists -- coherent sheaf cohomology module
• HH^ZZ(ProjectiveVariety,CoherentSheaf) -- cohomology of a coherent sheaf on a projective variety
• HH^ZZ(ProjectiveVariety,SheafMap)
• hilbertPolynomial(ProjectiveVariety) -- compute the Hilbert polynomial of the projective variety
• idealSheaf(ProjectiveVariety) -- see idealSheaf -- ideal sheaf of a projective variety
• isProjective(ProjectiveVariety) -- see isProjective -- whether a variety is projective
• tangentSheaf(ProjectiveVariety) -- see tangentSheaf -- tangent sheaf of a projective variety

For the programmer

The object ProjectiveVariety is a type, with ancestor classes Variety < MutableHashTable < HashTable < Thing.

The source of this document is in Varieties/doc-varieties.m2:17:0.